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Variability and Its Impact

Variability and Its Impact. Sunday Academy. Randomness. The word randomness is used to express uncertainty or lack of predictability There is randomness in every activity or event of the nature

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Variability and Its Impact

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  1. Variability and Its Impact Sunday Academy

  2. Randomness • The word randomness is used to express uncertainty or lack of predictability • There is randomness in every activity or event of the nature • A random process is a repeating process whose outcome is going to be different every time you repeat it

  3. Randomness (Examples) • Following examples represent random processes showing randomness (uncertainty) in outcome: • Die tossing experiment • There are six possible outcomes • Coin tossing experiment (tossing one coin or two coins) • In one coin tossing experiments—two possible outcomes • In two coin tossing experiment—four possible outcome • 100 meter race • Infinite number of outcomes • Manufacturing process • Infinite number outcomes

  4. Variability in Data • The randomness in the process introduces variability in output • Variability in process output can be visualized by plotting output data • Consider an example of 100 meter race (50 data points)

  5. Distribution of 100 Meter Race Data

  6. Variability in Data • Consider the example of manufacturing process A • Process mean 20 mm and standard deviation is 1.5

  7. Distribution of Manufacturing Process Output

  8. Distribution Parameters • To measure the central tendency: • Mean, Median, and Mode • To measure the total spread of the data: • Range and Standard Deviation (Std. Dev.)

  9. Symmetric Distribution Considering n number of data points: X1, X2, X3, … , Xn Mean—Average value of all data points Range—difference between largest and smallest data points Standard Deviation For symmetric distribution mean, median, and mode will have the same value

  10. Asymmetric Distribution Mode—data point which has highest frequency of occurrences Median—data point which divides area under distribution curve in two halves Calculating median If n number data points are ordered from smallest to largest: If n is odd, the sample median is the number in position If n is even, the sample median is the average of the number in positions and

  11. Calculation Example • Given the data set{13, 3, 10, 9, 7, 10, 12, 8, 6, 3, 9, 6, 11, 5, 9, 13, 8, 7, 7}find the mean, median and mode. • Rearrange data set from smallest to largest • Mean • Median • Mode

  12. Another example The population of Fargo city: adult male heights are on average 70 inches (5'10) with a standard deviation of 4 inches. Adult women are on average a bit shorter and less variable in height with a mean height of 65 inches (5'5) and standard deviation of 3.5 inches. If we took a large sample of men and women's heights and graphed the frequency of the heights we'd see something like the following:

  13. Performance Comparison (Impact of Variability) Two Players A and B competing for the 100 meter Olympic race. Their performance during practice sessions is shown below (30 recorded practice timing) Both players are giving average run time of 12 seconds with different variability (StdDev). For player A standard deviation is (0.5) and for player B Std. Dev. Is (0.25)

  14. Performance Comparison (Impact of Variability) If you want to bet on any of these two players, who would be your choice and why? A or B

  15. Impact of Variability on Product Quality Two different production processes Process A performance : Mean 20, StdDev 1.5 Process B performance: Mean 20, StdDev 0.5 Which process is more effective to produce good quality products?

  16. Impact of Variability on Product Quality Which process produces better quality product? A or B

  17. Impact of Variability on Business Performance • How a defective item affects business performance—chain reaction

  18. Activities • Three activities to demonstrate the concepts • Die tossing experiment to explain random processes • Sampling experiment to show random inspection process to find defective items and making decision on samples to accept or reject • Helicopter design experiment to build quality into design

  19. Activity 1: Die Tossing Experiment • To demonstrate random process concept • Toss a die and observe up face • Record the outcome in the table (mark each outcome as star in appropriate column of the table) • Repeat the exercise 50 times and record the outcome • Compare the distribution on outcomes of each group • Combined the outcome from each group and observe the distribution

  20. Activity 1: Die Tossing Experiment

  21. Activity 2: Sampling experiment • Demonstrating quality inspection process • Decide the decision rule (more than 5 % defective will result in rejecting the lot) • Select the appropriate lot size (25, 50 or 100) • Determine the sample size (say 10% of the of the lot size) • Use appropriate bowl paddle to get lot • Randomly pick a row from paddle for considering as a sample (say row 4), • Count the number of bad parts (colored beads) • Make decision on the lot

  22. Activity 2: Sampling experiment • Table to sampling data collection

  23. Activity 3: Helicopter Design

  24. Activity 3: Helicopter Design

  25. Activity 3: Helicopter Design

  26. Activity 3: Helicopter Design

  27. Just imagine the impact of variability here Questions and Discussion

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